Alpine Type S 6.5 question

In my 95 Grand Cherokee I'm running Alpine Type S 6.5 Coaxial's in the front doors and using the factory tweeters and amp for the highs. I plan on moving the Coax's to the back door and installing a set of 6.5 Type S components in front (already have these). Now I have two questions. Firstly, I ordered a Litebox4 amp which is 90w RMS x4. The speakers are rated at 80w RMS. Will I run into any issues with the amp putting out more than the speaker is rated at. Secondly, I'm not running a sub, even off the head unit the coax's really have a decent amount of bass, enough for the music that I listen to. My question though, certain songs just sound like the bass gives out, not necessarily distorted (ok maybe distorted), but I guess that it just can't go quite as low as it should. Would this be an issue with the speakers frequency response or the lack of power? As of now they are only getting 18w RMS from the head unit.

These speakers are rated at 70-22k hz. It's my understanding the lower the first number the deeper the sound of the bass can go? Now I know they won't sound like a sub and I'm ok with that, I need the trunk space and usually have the family riding with me, but would it be beneficial to go with a different speaker that offers maybe around 50-22k hz? Would the difference between 50-70 be that noticeable?

Edit: Is it safe to assume that a larger magnet will make the midbass hit harder as well? I know this was the case with subs, I'm assuming it still is. Been out of the loop for quite a while.